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#! /usr/bin/env python
from __future__ import print_function
from openturns import *
from math import *
TESTPREAMBLE()
RandomGenerator.SetSeed(0)
def cleanSymmetricTensor(inSymmetricTensor):
rowDim = inSymmetricTensor.getNbRows()
colDim = inSymmetricTensor.getNbColumns()
sheetDim = inSymmetricTensor.getNbSheets()
for i in range(rowDim):
for j in range(colDim):
for k in range(sheetDim):
inSymmetricTensor[i, j, k] = 1.e-4 * round(
1.e4 * inSymmetricTensor[i, j, k])
if (abs(inSymmetricTensor[i, j, k]) < 1.e-6):
inSymmetricTensor[i, j, k] = 0.0
return inSymmetricTensor
try:
# Create a collection of distribution
aCollection = DistributionCollection()
aCollection.add(Uniform(-1.0, 2.0))
aCollection.add(Gamma(2.0, 2.0, 0.0))
dim = aCollection.getSize()
# Create a copula
RCopula = CorrelationMatrix(dim)
for i in range(dim):
for j in range(i):
RCopula[i, j] = (i + j + 1.0) / (2.0 * dim)
# Instanciate one distribution object
distribution = ComposedDistribution(aCollection, NormalCopula(RCopula))
# Test for sampling
size = 10000
sample = distribution.getSample(size)
print("sample first=", repr(sample[0]), " last=", repr(sample[size - 1]))
print("sample mean=", repr(sample.computeMean()))
print("sample covariance=", repr(sample.computeCovariance()))
transform = distribution.getIsoProbabilisticTransformation()
print("isoprobabilistic transformation=", repr(transform))
transformedSample = transform(sample)
print("transformed sample first=", repr(
transformedSample[0]), " last=", repr(transformedSample[size - 1]))
print("transformed sample mean=", repr(transformedSample.computeMean()))
print("transformed sample covariance=", repr(
transformedSample.computeCovariance()))
# Test for evaluation
inverseTransform = distribution.getInverseIsoProbabilisticTransformation()
print("inverse isoprobabilistic transformation=", repr(inverseTransform))
transformedBackSample = inverseTransform(transformedSample)
print("transformed back sample first=", repr(
transformedBackSample[0]), " last=", repr(transformedBackSample[size - 1]))
print("transformed back sample mean=", repr(
transformedBackSample.computeMean()))
print("transformed back sample covariance=", repr(
transformedBackSample.computeCovariance()))
point = NumericalPoint(dim, 1.0)
print("point=", repr(point))
transformedPoint = transform(point)
print("transform value at point =", repr(transformedPoint))
print("transform gradient at point =", repr(
transform.gradient(point).clean(1e-6)))
print("transform gradient at point (FD)=", repr(CenteredFiniteDifferenceGradient(
1.0e-5, transform.getEvaluation()).gradient(point).clean(1e-6)))
print("transform hessian at point =", repr(
cleanSymmetricTensor(transform.hessian(point))))
print("transform hessian at point (FD) =", repr(cleanSymmetricTensor(
CenteredFiniteDifferenceHessian(1.0e-4, transform.getEvaluation()).hessian(point))))
print("inverse transform value at transformed point =",
repr(inverseTransform(transformedPoint)))
print("inverse transform gradient at transformed point =", repr(
inverseTransform.gradient(transformedPoint).clean(1e-6)))
print("inverse transform gradient at transformed point (FD)=", repr(CenteredFiniteDifferenceGradient(
1.0e-5, inverseTransform.getEvaluation()).gradient(transformedPoint).clean(1e-6)))
print("inverse transform hessian at transformed point =", repr(
cleanSymmetricTensor(inverseTransform.hessian(transformedPoint))))
print("inverse transform hessian at transformed point (FD) =", repr(cleanSymmetricTensor(
CenteredFiniteDifferenceHessian(1.0e-4, inverseTransform.getEvaluation()).hessian(transformedPoint))))
# Test for parameters
print("parameters gradient at point=", repr(
transform.parameterGradient(point)))
# Validation using finite difference
eps = 1e-5
factor = 1.0 / (2.0 * eps)
gradient = Matrix(5, 2)
# dT/dp0
coll = DistributionCollection(dim)
coll[0] = Uniform(-1.0 + eps, 2.0)
coll[1] = aCollection[1]
left = ComposedDistribution(
coll, NormalCopula(RCopula)).getIsoProbabilisticTransformation()
coll[0] = Uniform(-1.0 - eps, 2.0)
right = ComposedDistribution(
coll, NormalCopula(RCopula)).getIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[0, 0] = dTdp[0]
gradient[0, 1] = dTdp[1]
# dT/dp1
coll = DistributionCollection(dim)
coll[0] = Uniform(-1.0, 2.0 + eps)
coll[1] = aCollection[1]
left = ComposedDistribution(
coll, NormalCopula(RCopula)).getIsoProbabilisticTransformation()
coll[0] = Uniform(-1.0, 2.0 - eps)
right = ComposedDistribution(
coll, NormalCopula(RCopula)).getIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[1, 0] = dTdp[0]
gradient[1, 1] = dTdp[1]
# dT/dp2
coll = DistributionCollection(dim)
coll[0] = aCollection[0]
coll[1] = Gamma(2.0 + eps, 2.0, 0.0)
left = ComposedDistribution(
coll, NormalCopula(RCopula)).getIsoProbabilisticTransformation()
coll[1] = Gamma(2.0 - eps, 2.0, 0.0)
right = ComposedDistribution(
coll, NormalCopula(RCopula)).getIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[2, 0] = dTdp[0]
gradient[2, 1] = dTdp[1]
# dT/dp3
coll = DistributionCollection(dim)
coll[0] = aCollection[0]
coll[1] = Gamma(2.0, 2.0 + eps, 0.0)
left = ComposedDistribution(
coll, NormalCopula(RCopula)).getIsoProbabilisticTransformation()
coll[1] = Gamma(2.0, 2.0 - eps, 0.0)
right = ComposedDistribution(
coll, NormalCopula(RCopula)).getIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[3, 0] = dTdp[0]
gradient[3, 1] = dTdp[1]
# dT/dp4
coll = DistributionCollection(dim)
coll[0] = aCollection[0]
coll[1] = Gamma(2.0, 2.0, 0.0 + eps)
left = ComposedDistribution(
coll, NormalCopula(RCopula)).getIsoProbabilisticTransformation()
coll[1] = Gamma(2.0, 2.0, 0.0 - eps)
right = ComposedDistribution(
coll, NormalCopula(RCopula)).getIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[4, 0] = dTdp[0]
gradient[4, 1] = dTdp[1]
print("parameters gradient (FD) =", repr(gradient))
# Test for parameters
print("(inverse) parameters gradient at point=", repr(
inverseTransform.parameterGradient(point)))
# dT/dp0
coll = DistributionCollection(dim)
coll[0] = Uniform(-1.0 + eps, 2.0)
coll[1] = aCollection[1]
left = ComposedDistribution(
coll, NormalCopula(RCopula)).getInverseIsoProbabilisticTransformation()
coll[0] = Uniform(-1.0 - eps, 2.0)
right = ComposedDistribution(
coll, NormalCopula(RCopula)).getInverseIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[0, 0] = dTdp[0]
gradient[0, 1] = dTdp[1]
# dT/dp1
coll = DistributionCollection(dim)
coll[0] = Uniform(-1.0, 2.0 + eps)
coll[1] = aCollection[1]
left = ComposedDistribution(
coll, NormalCopula(RCopula)).getInverseIsoProbabilisticTransformation()
coll[0] = Uniform(-1.0, 2.0 - eps)
right = ComposedDistribution(
coll, NormalCopula(RCopula)).getInverseIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[1, 0] = dTdp[0]
gradient[1, 1] = dTdp[1]
# dT/dp2
coll = DistributionCollection(dim)
coll[0] = aCollection[0]
coll[1] = Gamma(2.0 + eps, 2.0, 0.0)
left = ComposedDistribution(
coll, NormalCopula(RCopula)).getInverseIsoProbabilisticTransformation()
coll[1] = Gamma(2.0 - eps, 2.0, 0.0)
right = ComposedDistribution(
coll, NormalCopula(RCopula)).getInverseIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[2, 0] = dTdp[0]
gradient[2, 1] = dTdp[1]
# dT/dp3
coll = DistributionCollection(dim)
coll[0] = aCollection[0]
coll[1] = Gamma(2.0, 2.0 + eps, 0.0)
left = ComposedDistribution(
coll, NormalCopula(RCopula)).getInverseIsoProbabilisticTransformation()
coll[1] = Gamma(2.0, 2.0 - eps, 0.0)
right = ComposedDistribution(
coll, NormalCopula(RCopula)).getInverseIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[3, 0] = dTdp[0]
gradient[3, 1] = dTdp[1]
# dT/dp4
coll = DistributionCollection(dim)
coll[0] = aCollection[0]
coll[1] = Gamma(2.0, 2.0, 0.0 + eps)
left = ComposedDistribution(
coll, NormalCopula(RCopula)).getInverseIsoProbabilisticTransformation()
coll[1] = Gamma(2.0, 2.0, 0.0 - eps)
right = ComposedDistribution(
coll, NormalCopula(RCopula)).getInverseIsoProbabilisticTransformation()
dTdp = (left(point) - right(point)) * factor
gradient[4, 0] = dTdp[0]
gradient[4, 1] = dTdp[1]
print("(inverse) parameters gradient (FD) =", repr(gradient))
except:
import sys
print("t_IsoProbabilisticTransformation_EllipticalCopula.py",
sys.exc_info()[0], sys.exc_info()[1])
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